14: Thermodynamic Tools I
- Page ID
- 519
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Module Goal: To establish the mathematical framework for thermodynamics of phase equilibrium.
- Module Objective: To highlight the importance of thermodynamic functions as functions of state.
The goal of this module, combined with all the background that we already have built on fluid behavior, is to establish a foundation for us to cultivate a culture of the appropriate utilization of thermodynamics.
- 14.1: Introduction
- This page outlines the significance of thermodynamics in science and engineering, emphasizing energy conversion through heat and motion. It highlights the importance of identifying systems and utilizing engineering judgment. The page categorizes thermodynamic problems into three types: property variations under constraints, external interactions for changes, and optimal pathways for goals.
- 14.2: Basic Definitions
- This page covers essential thermodynamics concepts such as systems and surroundings, classifying systems into open, closed, adiabatic, and isolated types based on heat and mass exchange. It differentiates thermodynamic properties into intensive and extensive categories and discusses homogeneous versus heterogeneous systems.
- 14.3: Thermodynamics of Systems of Constant Composition (Closed Systems)
- This page covers the fundamental principles of thermodynamics, focusing on the first and second laws and their relationship to internal energy, enthalpy, Gibbs free energy, and Helmholtz free energy in closed systems. It defines key equations for work, heat, and state function changes, emphasizing that internal energy changes are independent of the process path.
- 14.4: Functions of State or State Functions
- A function of state is one in which the differential change is determined only by the end states and not by intervening states. Most thermodynamic variables are state functions and hence property changes are determined by the end states and not by the process path. Notable exceptions are work and heat.
- 14.5: Mechanics of Manipulating a Function of State
- This page covers state functions in thermodynamics, highlighting that their changes rely only on initial and final states, independent of the path taken. It illustrates total changes through partial derivatives and includes an enthalpy example based on pressure and temperature. The discussion concludes with the "exactness condition," outlining the criteria that must be met for a function to be categorized as a state function, ensuring that its total differential is exact.
- 14.6: Computing Property Changes in Closed Systems
- This page covers essential thermodynamic concepts for closed systems, focusing on state functions such as internal energy, enthalpy, Gibbs free energy, and Helmholtz free energy, and their interdependencies based on measurable variables. It highlights the significance of state property changes and introduces Maxwell's relationships for simplifying thermodynamic equations. The page also defines heat capacities at constant pressure and volume, emphasizing their relevance for ideal gases.
- 14.7: Action Item
- This page outlines the instructions for a problem set assignment, detailing submission requirements, file formats, and access to the drop box. It specifies two problems: explaining the implications of the 1st and 2nd laws of thermodynamics in child-friendly terms and discussing the effects on process design if thermodynamic properties were not state functions. It also includes the grading timeline for the assignment.